Eisenstein series on affine Kac-Moody groups over function fields

Lee, Kyu-Hwan; Lombardo, Philip

doi:10.1090/S0002-9947-2013-06078-3

Eisenstein series on affine Kac-Moody groups over function fields
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by Kyu-Hwan Lee and Philip Lombardo PDF

Trans. Amer. Math. Soc. 366 (2014), 2121-2165 Request permission

Abstract:

In his pioneering work, H. Garland constructed Eisenstein series on affine Kac-Moody groups over the field of real numbers. He established the almost everywhere convergence of these series, obtained a formula for their constant terms, and proved a functional equation for the constant terms. In his subsequent paper, the convergence of the Eisenstein series was obtained. In this paper, we define Eisenstein series on affine Kac-Moody groups over global function fields using an adelic approach. In the course of proving the convergence of these Eisenstein series, we also calculate a formula for the constant terms and prove their convergence and functional equations.

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